Revisiting Operator $p$-Compact Mappings
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866908395597987840 |
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| author | Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel |
| author_facet | Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel |
| contents | We continue our study of the mapping ideal of operator $p$-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator $p$-compact mappings and matrix sets, specifically we provide a quantitative notion of operator $p$-compactness for the latter. In particular, we consider operator $p$-compactness in the bidual and its relation with this property in the original space. Also, we deepen our understanding of the connections between these mapping ideals and other significant ones (e.g., completely $p$-summing, completely $p$-nuclear). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18571 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting Operator $p$-Compact Mappings Chávez-Domínguez, Javier Alejandro Dimant, Verónica Galicer, Daniel Functional Analysis Operator Algebras 46L07 (primary), 47B10, 46B28 (secondary) 46L07 (primary), 47B10, 46B28 (secondary) 46L07 (primary), 47B10, 26B28 (secondary) We continue our study of the mapping ideal of operator $p$-compact maps, previously introduced by the authors. Our approach embraces a more geometric perspective, delving into the interplay between operator $p$-compact mappings and matrix sets, specifically we provide a quantitative notion of operator $p$-compactness for the latter. In particular, we consider operator $p$-compactness in the bidual and its relation with this property in the original space. Also, we deepen our understanding of the connections between these mapping ideals and other significant ones (e.g., completely $p$-summing, completely $p$-nuclear). |
| title | Revisiting Operator $p$-Compact Mappings |
| topic | Functional Analysis Operator Algebras 46L07 (primary), 47B10, 46B28 (secondary) 46L07 (primary), 47B10, 46B28 (secondary) 46L07 (primary), 47B10, 26B28 (secondary) |
| url | https://arxiv.org/abs/2405.18571 |